"Irlol" stands for "I Really Laughed Out Loud." Since people tend to send "lol" whenever they find something funny rather than when they actually have laughed out loud, irlol is for those time when someone has in real life, actually laughed aloud.

"Did you see that new dank meme going around the internet?"
"No, send me it."
*sends dank meme*
"IRLOL"